Properties

Label 5733.e
Number of curves $4$
Conductor $5733$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5733.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5733.e1 5733g3 \([1, -1, 1, -30659, -2058514]\) \(37159393753/1053\) \(90311725413\) \([2]\) \(9216\) \(1.2039\)  
5733.e2 5733g4 \([1, -1, 1, -8609, 280550]\) \(822656953/85683\) \(7348698545643\) \([2]\) \(9216\) \(1.2039\)  
5733.e3 5733g2 \([1, -1, 1, -1994, -29032]\) \(10218313/1521\) \(130450270041\) \([2, 2]\) \(4608\) \(0.85732\)  
5733.e4 5733g1 \([1, -1, 1, 211, -2572]\) \(12167/39\) \(-3344878719\) \([2]\) \(2304\) \(0.51075\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5733.e have rank \(1\).

Complex multiplication

The elliptic curves in class 5733.e do not have complex multiplication.

Modular form 5733.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2 q^{5} + 3 q^{8} - 2 q^{10} - 4 q^{11} - q^{13} - q^{16} + 2 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.